Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#14581751 |
| Sylow | C83 ⋊ C22×#117 |
1880 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 1157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309624, #35309635, #35309637, … |
| maximal normal subgroup of | #35309624, #35309635, #35309637, … |
| maximal quotient of | C22×#19127547, C22×C4×C22⋊Dic83, C22×C4×C4⋊Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17676);